Analyzing the Local Electronic Structure of Co3O4 Using 2p3d Resonant Inelastic X-ray Scattering

We present the cobalt 2p3d resonant inelastic X-ray scattering (RIXS) spectra of Co3O4. Guided by multiplet simulation, the excited states at 0.5 and 1.3 eV can be identified as the 4T2 excited state of the tetrahedral Co2+ and the 3T2g excited state of the octahedral Co3+, respectively. The ground states of Co2+ and Co3+ sites are determined to be high-spin 4A2(Td) and low-spin 1A1g(Oh), respectively. It indicates that the high-spin Co2+ is the magnetically active site in Co3O4. Additionally, the ligand-to-metal charge transfer analysis shows strong orbital hybridization between the cobalt and oxygen ions at the Co3+ site, while the hybridization is weak at the Co2+ site.


A. 2p XAS spectra background subtraction
shows the raw 2p XAS spectra (red), subtracted 2p XAS spectra (blue), and the background profile (black). We subtracted the background signal from the original XAS results, where the background signal contains edge jump(s), particles scattering, and linear signal. The subtracted spectra were normalized to the maximum of the Co L3-edge. The photon energy of RIXS beamline were calibrated to the spectra acquired in WERA beamline, where the calibration also applied to the incident energy of RIXS spectra.

B. Theoretical absorption background estimation
According to the tabulated data [s1], we can estimate the attenuation length for the individual elements of Co3O4 ( = 6.11 g/cm 3 ). The partial density of cobalt and oxygen elements ( and ) are 4.49 g/cm 3 and 1.62 g/cm 3 , respectively. So the attenuation lengths at 780 eV for the cobalt and oxygen elements in the Co3O4 are expected to be ~140 nm and ~700 nm, respectively. But the attenuation lengths at the absorption edge are likely overestimated using the Henke's table. For cobalt metal ( = 8.9 g/cm 3 ), the estimated attenuation length is ~75 nm but the experimental results indicate that the attenuation length was ~25 nm at the peak maximum [s2]. Thus, we estimated the value within the range from 25 nm to 140 nm for the attenuation length of cobalt element at 780 eV.
The weighting of is proportional to the inverse of the attenuation length that weighting of for Co and O are estimated to be 96-83% and 4-17% (attenuation lengths are 25-140 and 700 nm). For pure Co3O4, the background absorption ( ) at 780 eV is the contribution of the oxygen absorption (the contributions of other edges were omitted). Thus, a value of ~10% of the is suitable estimation for the .

C. Used parameters and the effective crystal field energy
Table S1-S4 give the used parameters. The Slater integrals F 2 dd, F 4 dd, F 2 pd , G 1 pd , and G 3 pd as well as the Udd and Upd are used to determine the Coulomb interaction. The Slater integrals were taken to an ionic scheme, where ~80%(75%) of the values from the Hartree-Fock approximation is used for the Co 2+ (Co 3+ ). The Udd and Upd values were set to the reference values. and describe the spinorbit interaction. The charge transfer energy ∆ and the hopping integrals V (e g ) / V t 2 (t 2g ) mimic the energy splitting between two configurations and the electron hopping intensity from one configuration to another one.
The crystal field energy 10Dq identifies the energy different between the e(eg) and the t2(t2g) orbitals in the Td(Oh) symmetry. Once the ligand-to-metal charge transfer is included, the total effective crystal energy 10Dqtot is composed by two different parts: (i) ionic crystal field energy of cobalt 3d shell (10Dqionic) and (ii) additional contribution caused by charge transfer and exchange interaction (10DqCT) [s4]. The 10Dqtot in currently work can be estimated by 1 A1g-1 T1g and 4 A2-4 T2 excited states energy for the octahedral Co 3+ and the tetrahedral Co 2+ sites, which are ~1.90 eV and ~−0.55 eV, respectively. The negative sign on the tetrahedral symmetry infers to the inverse of t2 and e orbitals with respect to the octahedral symmetry. In contrast, for the simulation considering the charge transfer and exchange interaction effects, the 10Dqionic should be further reduced to 1.15 eV and −0.1 eV for the octahedral Co 3+ site and tetrahedral Co 2+ site, respectively. Our theoretical crystal field energy values (obtained by LDA calculation) considered only the values applied on the Co 3d orbitals, which means the charge transfer induced crystal field energy splitting was not involved. Thus, only 10Dqionic of cobalt 3d shell has been compared in the main text. We note that the contraction induced by the core hole is applied to the whole valence state wave function (correspond to 10Dqtot), thus we applied the 10Dqtot value of the intermediate state is reduced by ~15% in comparison with the ground state [s3] (1.59 eV for the Co 3+ site and −0.47 for the Co 2+ site).
In the simulation, a 300 meV (FWHM) Lorentzian convoluting a 300 meV (FWHM) Gaussian was used to simulate the intrinsic broadening and the instrumental broadening of the incident beam. It provides a 0.6 eV total width. For the RIXS spectra, the same incident beam width was applied. In addition to it, a 50 meV (FWHM) Lorentzian convoluting a 60 meV (FWHM) Gaussian was used for the emitted beam, which implies a total width 0.11 eV. These values are comparable to the experimental setting. Nevertheless, we note that the intrinsic broadening was fixed to a value in the current simulation.  Figure S2 presents the comparison of the simulated spectra with and without ligand-to-metal charge transfer effect using the parameters in Table S1, S2 (using charge transfer parameters) and Table S3, S4 (using Slater reduction), respectively. Overall, the spectra look similar. The simulation including the ligand-to-metal charge transfer at both Co 2+ and Co 3+ sites shows better agreement. Figure S2: Comparison of the simulated spectra with and without ligand-to-metal charge transfer effect.

E. Estimating the differential orbital covalency of a cation from the cluster model
Including the ligand-to-metal charge transfer effect suggests that the ground state configuration is a mixture of the 3d orbit and ligand hole (L). We calculated the weight of configurations up to two ligand holes and list them in Table S5. Then, we further estimated the cation orbital covalency of Co 2+ and Co 3+ cations using the following relation [s4-s6]: where stands for the state corresponding to the e(eg) or t2(t2g) orbitals. 100% indicates to the target orbital which is dominated by the ionic configuration. The coefficient N is a renormalization factor of the number of holes in the orbit out of number of holes in 3dn configuration. For example, in the case of high-spin Co 2+ (Td), there are three holes in the t2 orbit out of three holes in 3d 7 configuration. Hence the renormalization factor is equal to one ( number of holes in 3 number of holes in 2 = 1). In contrast, the renormalization factor for the e orbit is meaningless because it is fully occupied (no hole exists). The is the percentages for the configurations which accept the elections transfer from ligand to the orbital. Note here that we only consider one electron transfer in the covalency estimation. is the percentages summation of all possible configurations involved in the hybridization, which is equal to one in this work. Thus, the cation orbital covalency of t2 orbital on the Co 2+ site and eg orbital on Co 3+ site are given as ~80% and ~50%, respectively. Table S3. The weight of configurations and orbital covalency in ground state (unit in %). Although the number of ligand holes is considered up to two in the spectral simulations, the covalency is estimated only using the configurations up to one ligand hole. |3d n > |3d n+1 L 1 > |3d n+2 L 2 > e(eg) covalency t2(t2g) covalency Co 2+ (3d 7 ) 79 20 1 100 80 Co 3+ (3d 6 ) 40 50 10 50 100